MODULAR OPERADS WITH CONNECTED SUM AND BARANNIKOV'S THEORY

Abstract

We introduce the connected sum for modular operads. This gives us a graded commutative associative product, and together with the BV bracket and the BV Laplacian obtained from the operadic composition and self-composition, we construct the full Batalin-Vilkovisky algebra.

The BV Laplacian is then used as a perturbation of the special deformation retract of formal functions to construct a minimal model and compute an effective action.

Keywords

• modular operads
• connected sum
• Batalin-Vilkovisky algebra
• homological perturbation lemma